STABILITY ANALYSIS OF PLATE OSCILLATION MODELING ALGORITHMS ON CELLULAR NEURAL NETWORKS

Abstract

Background. A fourth-order partial differential equation is considered, which describes the vibration of plates under the influence of an external force. Materials and methods. A finite-difference approximation in space and time of this equation leads to difference schemes in a non-stationary formulation. Results. An algorithm for the implementation of difference schemes is proposed with the calculation of increments to the solution at each time step, which makes it possible to avoid the accumulation of errors. The study of the stability of various difference schemes made it possible to derive a condition for the stability of an explicit scheme and to prove the absolute stability of implicit schemes. Conclusions. The performed analysis of explicit and implicit schemes shows the conditions for the stability of modeling algorithms.

Keywords

• biharmonic differential equation
• finite-difference approximation
• unsteady formulation
• stability of explicit and implicit difference schemes